Journal of Applied and Industrial Mathematics最新文献

Abstract

The reconstruction of physical properties of a medium from boundary measurements,known as inverse scattering problems, presents significant challenges. The present study aims tovalidate a newly developed convexification method for a 3D coefficient inverse problem in the caseof buried unknown objects in a sandbox, using experimental data collected by a microwavescattering facility at The University of North Carolina at Charlotte. Our study considers theformulation of a coupled quasilinear elliptic system based on multiple frequencies. The system canbe solved by minimizing a weighted Tikhonov-like functional, which forms our convexificationmethod. Theoretical results related to the convexification are also revisited in this work.

We consider a competitive facility location model where competing parties (Leader andFollower) make decisions considering changes of the set of customers happening during the planinghorizon consisting a known number of time periods. It is assumed that the Leader makes adecision on opening their facilities at the beginning of the planning horizon, while the Follower canrevise their decision in each time period. In the present paper, we study perspectives to apply amethod for finding the best solution that is based on using HP-relaxation of the bilevel problemconsidered. The key element of this method is construction of additional inequalitiesstrengthening the HP-relaxation and computation of upper bounds for the objective function ofthe problem. In the paper, we propose new families of additional constraints to strengthen theHP-relaxation that allow computing nontrivial upper bounds.

The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationarysolutions are found on the invariant set of the zero level of the area integral, and their stability isanalyzed. For the case where the suspension point coincides with the center of mass and theaction of a gyroscopic moment is of a special type, integration by quadratures is performed.

Bent functions at the minimum distance( 2^n ) from a given bent function of( 2n ) variables belonging to the Maiorana–McFarland class( mathcal {M}_{2n} ) are investigated. We provide a criterion for a function obtained using theaddition of the indicator of an( n )-dimensional affine subspace to a given bent function from( mathcal {M}_{2n} ) to be a bent function as well. In other words, all bent functions at theminimum distance from a Maiorana–McFarland bent function are characterized. It is shown thatthe lower bound( 2^{2n+1}-2^n ) for the number of bent functions at the minimum distance from( f in mathcal {M}_{2n} ) is not attained if the permutation used for constructing( f ) is not an APN function. It is proved that for any prime( ngeq 5 ) there exist functions in( mathcal {M}_{2n} ) for which this lower bound is accurate. Examples of such bent functions arefound. It is also established that the permutations of EA-equivalent functions in( mathcal {M}_{2n} ) are affinely equivalent if the second derivatives of at least one of thepermutations are not identically zero.

The set of vertices of a graph is called distance-( k ) independent if the distance betweenany two of its vertices is greater than some integer( k geq 1 ). In this paper, we describe( n )-vertex trees with a given diameter( d ) that have the maximum and minimum possible number of distance-( k ) independent sets among all such trees. The maximum problem is solvable forthe case of( 1 < k < d leq 5 ). The minimum problem is much simpler and can be solved for all( 1 < k < d < n ).

The article describes a method for determining the heat flux density on the surface of athin foil that is inaccessible for thermal imaging measurements based on thermal imaging data onthe other side of the foil, available for measurements. Mathematically, the problem is reduced tosolving the Cauchy problem for an elliptic equation, which is ill-posed. The problem is solvedusing noise smoothing in the initial temperature field and a correct restriction on the number ofexpansion terms in the Fourier series. According to the measurement results, the heat flux densityreaches its maximum in the area of the contact line and amounts to( 4200~text {W}/text {m}^2 ).

We consider an algorithm for monitoring the process of sputter deposition of opticalcoatings based on the analysis of sample data of broadband measurements for a fixed set ofwavelengths. On the one hand, the considered algorithm uses broadband measurement data,which is an advantage compared to using only monochromatic measurement data for one fixedwavelength, and on the other hand, it is fast compared to algorithms that use complete broadbandmeasurement data. It has been demonstrated that the proposed algorithm allows one to obtainfairly accurate estimates of the layer thicknesses in deposited multilayer optical coatings.

Due to the development of quantum computing, there is a need for the development andanalysis of cryptosystems resistant to attacks using a quantum computer (post-quantumcryptography algorithms). The security of many well-known post-quantum cryptosystems basedon lattice theory depends on the complexity of solving the shortest vector problem (SVP). In thispaper, a model of quantum oracle developed from Grover’s algorithm is described to implementa hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used forattacks on cryptosystems whose security depends on solving the SVP. Upper bounds for thenumber of qubits and the depth of the circuit were obtained for two implementations of theproposed quantum oracle model: minimizing the number of qubits and minimizing the circuitdepth. The complexity of implementing the proposed quantum oracle model to attackpost-quantum lattice-based cryptosystems that are finalists of the NIST post-quantumcryptography competition is analyzed.

We study a mathematical model of competition between two populations described by asystem of nonlinear differential reaction–diffusion–advection equations. The taxis is introduced tomodel the heterogeneity of the total resource and the nonuniform distribution of both species. Weanalyze the role of the taxis in the area occupancy. The maps of migration parameterscorresponding to various variants of competitive exclusion and coexistence of species arecalculated. Using the theory of cosymmetry, we find parametric relations under whichmultistability arises. In a computational experiment, population scenarios with a violation ofcosymmetry were studied.

A numerical study of the process of cooling a substrate under the conditions ofevaporation of pure vapor from the surface of a liquid film and droplets was carried out. Thelattice Boltzmann method was used for modeling such a two-phase system taking into account thethermal conductivity of the substance and the evaporation. We used the van der Waals equationof state describing the liquid–vapor phase transition. A new method is proposed for setting theboundary conditions on a flat surface for modeling the contact wetting angles in the latticeBoltzmann method. The latent heat of phase transition is taken into account. It is shown that theprocess depends on the film thickness and the rate of vapor removal from the film surface. Thecases of forced outflow of vapor, as well as the method of vapor condensation on a cooledcondenser are considered. It is shown that the heat flux from the substrate increases sharply inthe vicinity of the droplet contact lines. A comparison is made of the heat fluxes during theevaporation of the film and droplets on substrates with different wettabilities.